Bubble-point surface

From the three distinct 2D cross-sectional views (7.41a), (7.42), (7.43) of the P-T-x surface, we can now visualize the full 3D form of the surface as shown in Fig. 7.8. The surface is seen to resemble a curved envelope, clipped at each end to reveal the inside of the envelope through the hatched holes. Viewed toward the P—T plane, only the curved edge of the envelope is seen, as in (7.41a). However, viewed toward the P-xB plane or the T-xB plane, the inside of the envelope is seen as the hatch marks in (7.42) or (7.43), respectively. The upper P-T-x surface of the envelope is called the bubble-point surface, in reference to the first vapor bubbles that are seen as the liquid is heated to its boiling point. The P-T-xBap underside of the envelope is correspondingly called the dew-point surface, in reference to the first dewy droplets of liquid as the vapor is cooled to its condensation temperature. Although we normally see only the flat P-T, P-xB, or T-xb projections on the blackboard or book page, it is useful to keep in mind the full 3D form of the P-T-xB surface that underlies these 2D projections of the / = 3 system. 

The region lying above the upper surface of Fig. 12.1 is the subcooled-liquid region that below the under surface is the superheated-vapor region. The interior space between the two surfaces is the region of coexistence of both liquid and vapor phases. If one starts with a liquid at F and reduces the pressure at constant temperature and composition along vertical line FG, the first bubble of vapor appears at point L, which lies on the upper surface. Thus, L is a bubble point, and the upper surface is the bubble-point surface. The state of the vapor bubble in equilibrium with the liquid at L must be represented by a point on the under surface at the temperature and pressure of L. This point is indicated by the letter V. Line VL is an example of a tie line, which connects points representing phases in equilibrium. 

Equations of state (ES) may be divided between those that are analytic and those that are not. Analytic equations of the form P(p,T,[Zi]) cannot provide an accurate description of thermodynamic properties in the critical region whether for the pure components or their mixtures. Scaled ES are non-analytlc in the usual P (p,T) coordinates but assume analyticlty in y(p,T) for pure components. The choice of variables for a scaled ES for a mixture is not well-defined although Leung and Griffiths (1 ) have used P(T,[uil) with success on the 3He- He system. Phase diagrams are simplier in such coordinates as the bubble-point surface and dew-point surface collapse into a single sheet. 

If the reservoir pressure remains above the bubble point then any gas liberated from the oil must be released in the tubing and the separators, and will therefore appear at the surface. In this case the producing gas oil ratio (Rp) will be equal to R. i.e. every stock tank barrel of oil produced liberates Rs scf of gas af surface. 

The collection of representative reservoir fluid samples is important in order to establish the PVT properties - phase envelope, bubble point, Rg, B, and the physical properties - composition, density, viscosity. These values are used to determine the initial volumes of fluid in place in stock tank volumes, the flow properties of the fluid both in the reservoir and through the surface facilities, and to identify any components which may require special treatment, such as sulphur compounds. 

Fluid samples may be collected downhole at near-reservoir conditions, or at surface. Subsurface samples are more expensive to collect, since they require downhole sampling tools, but are more likely to capture a representative sample, since they are targeted at collecting a single phase fluid. A surface sample is inevitably a two phase sample which requires recombining to recreate the reservoir fluid. Both sampling techniques face the same problem of trying to capture a representative sample (i.e. the correct proportion of gas to oil) when the pressure falls below the bubble point. 

Sampling saturated reservoirs with this technique requires special care to attempt to obtain a representative sample, and in any case when the flowing bottom hole pressure is lower than the bubble point, the validity of the sample remains doubtful. Multiple subsurface samples are usually taken by running sample bombs in tandem or performing repeat runs. The samples are checked for consistency by measuring their bubble point pressure at surface temperature. Samples whose bubble point lie within 2% of each other may be sent to the laboratory for PVT analysis. 

In the solution gas drive case, once production starts the reservoir pressure drops very quickly, especially above the bubble point, since the compressibility of the system is low. Consequently, the producing wells rapidly lose the potential to flow to surface, and not only is the plateau period short, but the decline is rapid. 

Membrane Characterization The two important characteristics of a UF membrane are its permeability and its retention characteristics. Ultrafiltration membranes contain pores too small to be tested by bubble point. Direc t microscopic observation of the surface is difficult and unreliable. The pores, especially the smaller ones, usually close when samples are dried for the electron microscope. Critical-point drying of a membrane (replacing the water with a flmd which can be removed at its critical point) is utihzed even though this procedure has complications of its own it has been used to produce a Few good pictures. 

The effect of the mobile-phase composition on the operation of the different interfaces is an important consideration which will be discussed in the appropriate chapter of this book but mobile-phase parameters which affect the operation of the interface include its boiling point, surface tension and conductivity. The importance of degassing solvents to prevent the formation of bubbles within the LC-MS interface must be stressed. 

Bubble Point Large areas of microfiltration membrane can be tested and verified by a bubble test. Pores of the membrane are filled with liquid, then a gas is forced against the face of the membrane. The Young-Laplace equation, AF = (4y cos Q)/d, relates the pressure required to force a bubble through a pore to its radius, and the interfacial surface tension between the penetrating gas and the liquid in the membrane pore, y is the surface tension (N/m), d is the pore diameter (m), and P is transmembrane pressure (Pa). 0 is the liquid-solid contact angle. For a fluid wetting the membrane perfectly, cos 0 = 1. 

The membrane pore size can be calculated from the measured bubble point Pj, by using the dimensionally consistent Equation 10.9. This is based on a simphstic model (Figure 10.6) that equates the air pressure in the cyhndrical pore to the cosine vector of the surface tension force along the pore surface [6] ... 

Figure 7.8 Three-dimensional curved envelope of the binary fluid P-T-xB surface (left), showing the upper bubble-point (liquid) surface, the lower dew-point (vapor) surface, and the hatched inside of the envelope, together with the three 2D projections (right) that result from slicing the envelope through the plane of constant temperature (upper), pressure (middle), or composition (lower).

Note that the propane vapor is still condensing to propane liquid at 120°F. The condensed liquid is in intimate contact with the propane vapor, as it drips off the outside surface of the colder condenser tubes. The saturated propane vapor condenses directly to saturated propane liquid at 120°F. The saturated, or bubble-point, liquid then drips from the condensation zone of the condenser into the subcooling zone of the condenser. This is the zone where the tubes are submerged in liquid. 

The tower overhead vapor, shown in Fig. 13.6, condenses to a liquid on the outside of the cold condenser tubes. The liquid drips off the tubes. These droplets of liquid are in close contact with the saturated vapor in the condenser shell. This means that the liquid is in equilibrium with the vapor. The condensed liquid is therefore, initially, at its bubble-point temperature. This liquid accumulates in the bottom of the condenser s shell. The submerged tubes then must subcool this liquid. Part of the surface area of the condenser is hence devoted to subcooling liquid, and part is devoted to condensing vapor. 

Consider a black oil at a reservoir pressure above the bubble point. Production into the wellbore will consist solely of liquid. During the trip to the surface and through surface equipment to the stock tank, the dissolved gas will come out of solution. This gas will appear as separator gas and stock-tank vent gas. Typical surface facilities for a black oil are shown in Figure 13-1. 

The quantity of gas produced with each barrel of stock-tank oil will remain constant as long as reservoir pressure is above bubble-point pressure. The usual methods of keeping track of surface gas and stock-tank oil will cause some variance in the producing gas-oil ratio, but the trend will be constant. 

As production proceeds, reservoir pressure will decrease. When bubble-point pressure is reached, gas forms in the pore space. At first ftmfree gas does not move. However, as pressure continues to decrease, the volume of gas in the pore space increases, and the gas begins to move to the wellbore. At this point the producing gas-oil ratio at the surface increases since it consists of both dissolved gas and free gas. 

Figure 11-1 gives a correlation for bubble-point pressure.1 3 The correlation is entered with solution gas-oil ratio derived from early production history. If the information is based on gas sales, the gas-oil ratio must be adjusted for stock-tank vent gas and for any gas lost or used in surface operations. 

With large-surface-area membrane filter media, the interpretation of the true bubble point can be further complicated because of the diffusion of the test gas through the media. Because the filter media are more than 70% void space, a liquid-wetted membrane is virtually a thin film of liquid across which a test gas will diffuse, governed by Fick s law. 

The bubble point test is simple, quick and reliable and is by far the most widely used method of characterizing microfiltration membranes. The membrane is first wetted with a suitable liquid, usually water for hydrophilic membranes and methanol for hydrophobic membranes. The membrane is then placed in a holder with a layer of liquid on the top surface. Air is fed to the bottom of the membrane, and the pressure is slowly increased until the first continuous string of air bubbles at the membrane surface is observed. This pressure is called the bubble point pressure and is a characteristic measure of the diameter of the largest pore in the membrane. Obtaining reliable and consistent results with the bubble point test requires care. It is essential, for example, that the membrane be completely wetted with the test liquid this may be difficult to determine. Because this test is so widely used by microfiltration membrane manufacturers, a great deal of work has been devoted to developing a reliable test procedure to address this and other issues. The use of this test is reviewed in Meltzer s book [3],... 

The concentrations of both the liquid phase, xB, and the vapor phase, yB, are determined by the pressure. The line relating vapor pressure to liquid-phase concentration is called the bubble-point line, because when the pressure on the liquid is reduced to this value, bubbles appear. The lower line, which relates vapor pressure to the vapor-phase concentration, is called the dew-point line because when vapor is compressed to give this pressure, liquid droplets appear on surfaces. 

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